While the BBC used this as an excuse to tour other Russian colloquialisms, no mention was made of the "American cousin" of Putin's remark:

Never try to teach a pig to sing. It wastes your time and annoys the pig.

This seems to have quite a tradition behind it. It has been attributed to Mark Twain, but I have yet to encounter a printed source for it in the Twain canon. On the other hand, it does appear in print in Robert Heinlein, where it is one of the maxim of Lazarus Long, the protagonist of Time Enough for Love. It is not hard to imagine that Putin might be a Heinlein fan!